# MultiVariableCalculusFunctions(S, F, FLAF, FLAS)¶

MultiVariableCalculusFunctions Package provides several functions for multivariable calculus. These include gradient, hessian and jacobian, divergence and laplacian. Various forms for banded and sparse storage of matrices are included.

bandedHessian: (F, FLAS, NonNegativeInteger) -> Matrix F

bandedHessian(v, xlist, k) computes the hessian, the matrix of second partial derivatives, of the scalar field v, v a function of the variables listed in xlist, k is the semi-bandwidth, the number of nonzero subdiagonals, 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix, dimensions k+1 by #xlist, whose rows are the vectors formed by diagonal, subdiagonal, etc. of the real, full-matrix, hessian. (The notation conforms to LAPACK/NAG-F07 conventions.)

bandedJacobian: (FLAF, FLAS, NonNegativeInteger, NonNegativeInteger) -> Matrix F

bandedJacobian(vf, xlist, kl, ku) computes the jacobian, the matrix of first partial derivatives, of the vector field vf, vf a vector function of the variables listed in xlist, kl is the number of nonzero subdiagonals, ku is the number of nonzero superdiagonals, kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix, dimensions kl+ku+1 by #xlist. The upper triangle is in the top ku rows, the diagonal is in row ku+1, the lower triangle in the last kl rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-F07 conventions.)

divergence: (FLAF, FLAS) -> F

divergence(vf, xlist) computes the divergence of the vector field vf, vf a vector function of the variables listed in xlist.

gradient: (F, FLAS) -> Vector F

gradient(v, xlist) computes the gradient, the vector of first partial derivatives, of the scalar field v, v a function of the variables listed in xlist.

hessian: (F, FLAS) -> Matrix F

hessian(v, xlist) computes the hessian, the matrix of second partial derivatives, of the scalar field v, v a function of the variables listed in xlist.

jacobian: (FLAF, FLAS) -> Matrix F

jacobian(vf, xlist) computes the jacobian, the matrix of first partial derivatives, of the vector field vf, vf a vector function of the variables listed in xlist.

laplacian: (F, FLAS) -> F

laplacian(v, xlist) computes the laplacian of the scalar field v, v a function of the variables listed in xlist.